Abstract: We investigate the radio and gamma-ray beaming properties of normal andmillisecond pulsars by selecting two samples from the known populations. Thefirst, Sample G, contains pulsars which are detectable in blind searches ofgamma-ray data from the Fermi Large Area Telescope. The second, Sample R,contains pulsars detectable in blind radio searches which have spin-downluminosities Edot > 10^{34} erg-s. We analyse the fraction of thegamma-ray-selected Sample G which have detectable radio pulses and the fractionof the radio-selected Sample R which have detectable gamma-ray pulses. Twentyof our 35 Sample G pulsars have already observed radio pulses. This rules outlow-altitude polar-cap beaming models if, as is currently believed, gamma-raybeams are generated in the outer magnetosphere and are very wide. We furtherfind that, for the highest-Edot pulsars, the radio and gamma-ray beams havecomparable beaming factors, i.e., the beams cover similar regions of the sky asthe star rotates. For lower-Edot gamma-ray emitting pulsars, the radio beamshave about half of the gamma-ray sky coverage. These results suggest that, forhigh-Edot young and millisecond pulsars, the radio emission originates in widebeams from regions high in the pulsar magnetosphere, probably close to thenull-charge surface and to the gamma-ray emitting regions. Furthermore, itsuggests that for these high-Edot pulsars, as in the gamma-ray case, featuresin the radio profile represent caustics in the emission beam pattern.